Question

RectangleABCD has vertices at A(– 3, 1),B(– 2, – 1),C(2, 1), andD(1, 3). What is the area, in square units, of this rectangle? A.10 B.5 C.25 D.100

Answer 1

Option A.
`10\ units^(2)`

Explanation:

we know that

The area of the rectangle is equal to

A=LW

where

L is the length of rectangle

W is the width of rectangle

we have

`A(-3,1),B(-2,-1),C(2,1),D(1,3)`

Plot the vertices

see the attached figure

L=AD=BC

W=AB=DC

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Find the distance AD

`A(-3,1),D(1,3)`

substitute in the formula

`AD=\sqrt{(3-1)^(2)+(1+3)^(2)}`

`AD=\sqrt{(2)^(2)+(4)^(2)}`

`AD=√(20)`

`AD=2√(5)\ units`

Find the distance AB

`A(-3,1),B(-2,-1)`

substitute in the formula

`AB=\sqrt{(-1-1)^(2)+(-2+3)^(2)}`

`AB=\sqrt{(-2)^(2)+(1)^(2)}`

`AB=√(5)`

`AB=√(5)\ units`

Find the area

`A=(2√(5))*(√(5))=10\ units^(2)`